It is interesting to note that the action here is different from the ones obtained by the flat limit of the Liouville CFT. Liouville theory has been used in the boundary dynamics of AdS\(_3\)  at the classical level [1]}, [2]}. The flat versions have been used to provide a similar holographic description of 3d flat spacetime. It would be of interest to figure out what this new version leads to in terms of flat holography.
